Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = 6$ $a_i = \dfrac{3}{2}a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $6$ and the common ratio is $\dfrac{3}{2}$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = 6 \cdot \dfrac{3}{2} = 9$.